Our main focus is the operator \(H_V:=H+V\) . It makes sense as a bounded operator \(H_V:{H}_+\rightarrow {H}_-\) . Furthermore, as the symmetric quadratic form \(Q_V\)  is \(H\) -form compact, it is \(H\) -form bounded with zero \(H\) -bound (see [1]}). Therefore, by the KLMN theorem (see, e.g., [2]}, [3]}) the restriction of \(H_V\)  to \(\operatorname{dom}(H_V):=H_V^{-1}({H})\)  is a bounded from below selfadjoint operator on \({H}\)  whose quadratic form is precisely \(Q_H+Q_V\) .
